Prefab is a separate scene that can be instantiated to some other scene, while preserving links between properties between instances and its parent prefab. Prefabs allow you to create a part of a scene and create multiple instances of it in some other scenes.
Let's quickly check what that means on practice. The engine has a prefab system which allows you to build hierarchical scenes which can include any number of other scenes as child scenes. Child scenes can have their own child scenes and so on. This is very efficient decoupling mechanism that allows you to put pieces of the scene in separate scenes (prefabs) and modify them independently. The changes in child scenes will be automatically reflected to all parent scenes. Here is the very simple example of why this is important: imagine you need to populate a town with 3D models of cars. Each kind of car has its own 3D model and for example, a collision body that won't allow the player to walk through cars. How would you do this? The simplest (and dumbest) solution is to copy dozens of car models in the scene, and you're done. Imagine that now you need to change something in your car, for example, add a trunk that can be opened. What will you do? Of course, you should "iterate" over each car model and do the required changes, you simply don't have any other option. This will eat huge amount of time and in general it is very non-productive.
This is where prefabs will save you hours of work. All you need to do is to create a car prefab and instantiate it multiple times in your scene. When you'll need to change something in the car, you simply go to the prefab and change it. After that every prefab instance will have your changes!
All you need to do is to make a scene in the editor with all required objects and save it! After that, you can use the scene in other scenes and just do its instantiation, as in usual 3D models. You can either instantiate it from the editor by drag'n'drop a prefab to scene previewer, or do standard model resource instantiation
As already mentioned in the intro section, instances inherit properties from their parent prefabs. For example, you can change position of an object in prefab and every instance will reflect that change - the object's instances will also move. This works until there's no manual change to a property in instance, if you do so, your change is considered with higher priority. Such feature allows you to tweak instances, add some unique details to them, but keep generic properties from parent prefabs.
Prefabs can have other prefab instances inside it. This means that you can, for example, create a room populated with instances of other prefabs (bookshelves, chairs, tables, etc.) and then use the room prefab to build a bigger scene. The changes in the base prefabs will be reflected in their instances, regardless of how deep the hierarchy is.
Prefab entities can have script assigned, the engine will create respective instances when you'll instantiate a prefab in a scene. The main difference here, is in property inheritance - current version of the engine (0.27) does not support inheritance for properties in scripts. This means, that making hierarchical prefabs with scripts could be problematic, there is no way to create a basic prefab with scripts and change properties of scripts in derived prefabs while keeping the inheritance.